Finite Group Databasebeta

← C2×#21458196 #30558458

Subgroups — C2×#21458196 #30558458

Order 15616.

1930 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840460C211yesmaximal, characteristic
2C2×#16840454C211yesmaximal, characteristic, complemented
3#21458196C2116yesmaximal, direct product factor
4C2×#16840163C211yesmaximal, characteristic, complemented
5C2×#16840102C211yesmaximal, characteristic, complemented
6C2×#16840089C211yesmaximal, characteristic, complemented
7C2×#16840076C211yesmaximal, characteristic, complemented
8C2×#16840071C211yesmaximal, characteristic, complemented
9C2×#16840065C211yesmaximal, characteristic, complemented
10C2×#16839994C211yesmaximal, characteristic, complemented
11C2×#16839993C211yesmaximal, characteristic, complemented
12C2×#16839847C211yesmaximal, characteristic, complemented
13C2×#16839825C211yesmaximal, characteristic, complemented
14C2×#16839799C211yesmaximal, characteristic, complemented
15C22×#14519708C211yesmaximal, characteristic, complemented
16C2×C61×#484C211yesmaximal, characteristic, complemented
17C22×#11758201C2211yescharacteristic
18C23×#92418C2211yescharacteristic
19C22×C8×D61C2211yescharacteristic
20#16840460—24no—
21#16840460C2218yes—
22#16840454—24no—
23#16840454C2218yescomplemented
24C2×#14519772—21no—
25C2×#14519772—21no—
26C2×#14519768—21no—
27C2×#14519768C2211yescharacteristic
28C2×#14519768C2211yescharacteristic
29C2×#14519762—21no—
30C2×#14519761—21no—
31C2×#14519753C2211yescharacteristic
32C2×#14519752C2211yescharacteristic
33C2×#14519751—21no—
34C2×#14519751C2211yescharacteristic
35C2×Q8×Dic61C2211yescharacteristic
36C2×#14519739C2211yescharacteristic
37C2×C4×C22⋊D61—21no—
38C2×C4×C22⋊D61C2211yescharacteristic
39C2×#14519735C2211yescharacteristic
40C2×#14519735C2211yescharacteristic
41C2×#14519733—21no—
42C22×C4⋊Dic61C2211yescharacteristic
43#16840163C2218yescomplemented
44#16840102C2218yescomplemented
45#16840089C2218yescomplemented
46#16840076C2218yescomplemented
47#16840071C2218yescomplemented
48#16840065C2218yescomplemented
49#16839994C2218yescomplemented
50#16839993C2218yescomplemented
51#16839847C2218yescomplemented
52#16839825C2218yescomplemented
53#16839799C2218yescomplemented
54C2×#14519711C2211yescharacteristic
55C2×#14519711C2211yescharacteristic
56C2×#14519708C2211yescharacteristic
57C2×#14519708C2211yescharacteristic
58C2×#14519708C2211yescharacteristic
59C2×#14519708C2211yescharacteristic
60C2×#14519708C2211yescharacteristic
61C2×#14519708C2218yescomplemented
62C2×#14519706C2211yescharacteristic
63C2×#14519701C2211yescharacteristic
64C2×#14519699C2211yescharacteristic
65C2×#14519699C2211yescharacteristic
66C2×#14519697C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C2×C22⋊Q8×C61C2211yescharacteristic
70C22×C4⋊C4×C61C2211yescharacteristic
71C61×#484C2218yescomplemented
72C2×#107×C61C2211yescharacteristic
73C2×#107×C61C2211yescharacteristic
74C2×#103×C61C2211yescharacteristic
75C2×#103×C61C2211yescharacteristic
76C2×C22⋊C8×C61C2211yescharacteristic
77C22×D244—21no—
78C22×D244C2311yescharacteristic
79C22×C22⋊D61—21no—
80C22×C22⋊D61D411yescharacteristic
81C23×Dic61—21no—
82C22×C4×D61—21no—
83C22×C4×D61C2311yescharacteristic
84C2×#11758201—24no—
85C2×#11758201C2314yes—
86C22×#92418—24no—
87C22×#92418C2311yescharacteristic
88C22×#92418C2314yes—
89C22×#92418C2311yescharacteristic
90C2×C8×D61—24no—
91C2×C8×D61C2314yes—
92#14519772—28no—
93#14519772—28no—
94#14519768—28no—
95#14519768—22no—
96#14519768—22no—
97#14519768C2314yes—
98#14519768C2314yes—
99#14519762—28no—
100#14519761—28no—
101#14519753—22no—
102#14519753C2314yes—
103#14519752—22no—
104#14519752C2314yes—
105#14519751—22no—
106#14519751—28no—
107#14519751C2314yes—
108Q8×Dic61—22no—
109Q8×Dic61C2314yes—
110#14519739—22no—
111#14519739C2314yes—
112C4×C22⋊D61—28no—
113C4×C22⋊D61D414yes—
114C4×C22⋊D61C2314yes—
115#14519735—22no—
116#14519735—22no—
117#14519735C2314yes—
118#14519735C2314yes—
119#14519733—28no—
120C2×C4⋊Dic61—22no—
121C2×C4⋊Dic61—21no—
122C2×C4⋊Dic61—21no—
123C2×C4⋊Dic61—21no—
124C2×C4⋊Dic61—21no—
125C2×C4⋊Dic61C2314yes—
126C2×C4⋊Dic61C2311yescharacteristic
127C2×C4⋊Dic61C2311yescharacteristic
128C2×C4⋊Dic61C2311yescharacteristic
129C2×#11758196—21no—
130C2×#11758196—21no—
131C2×#11758196—21no—
132C2×#11758196D411yescharacteristic
133C2×C22⋊Dic61D411yescharacteristic
134C2×#11758198—21no—
135C2×#11758198—21no—
136C2×#11758198—21no—
137C2×#11758198—21no—
138C2×#11758198—21no—
139C2×#11758198—21no—
140C2×#11758198D411yescharacteristic
141C2×C4×Dic61—21no—
142C2×C4×Dic61—21no—
143C2×C4×Dic61—21no—
144C2×C4×Dic61C2311yescharacteristic
145#14519711C2314yes—
146#14519711C2314yes—
147#14519708C2314yes—
148#14519708C2314yes—
149#14519708C2314yes—
150#14519708C2314yes—
151#14519708C2314yes—
152#14519706C2314yes—
153#14519701C2314yes—
154#14519699C2314yes—
155#14519699C2314yes—
156#14519697C2314yes—
157#14519689C2314yes—
158C8×Dic61C2314yes—
159C22×Q8×C61C2311yescharacteristic
160C23×C4×C61—21no—
161C23×C4×C61C2311yescharacteristic
162C22×C8×C61C2311yescharacteristic
163C22×C8×C61C2311yescharacteristic
164C22⋊Q8×C61—22no—
165C22⋊Q8×C61C2314yes—
166C2×C4⋊C4×C61—22no—
167C2×C4⋊C4×C61—21no—
168C2×C4⋊C4×C61—21no—
169C2×C4⋊C4×C61C2314yes—
170C2×C4⋊C4×C61C2311yescharacteristic
171C2×C4⋊C4×C61C2311yescharacteristic
172C2×C4⋊C4×C61C2311yescharacteristic
173C2×C22⋊C4×C61—21no—
174#107×C61C2314yes—
175#107×C61C2314yes—
176#103×C61C2314yes—
177#103×C61C2314yes—
178C22⋊C8×C61C2314yes—
179C24×C61C2×D411yescharacteristic
180C23×D61—21no—
181C23×D61C2×D411yescharacteristic
182C2×Q8×C61—21no—
183C2×Q8×C61—22no—
184C2×Q8×C61—22no—
185C2×Q8×C61C2412yes—
186C22×C4×C61—22no—
187C22×C4×C61—22no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—24no—
193C22×C4×C61—82no—
194C22×C4×C61C2×D411yescharacteristic
195C22×C4×C61C2×D412yes—
196C22×C4×C61C2412yes—
197C22×C4×C61C2411yescharacteristic
198C2×C22⋊D61—24no—
199C2×C22⋊D61—24no—
200C2×C22⋊D61—44no—
201C2×C22⋊D61C2×D414yes—
202C22×Dic61—21no—
203C22×Dic61—21no—
204C22×Dic61—24no—
205C22×Dic61—21no—
206C22×Dic61—44no—
207C22×Dic61C2×D411yescharacteristic
208C22×Dic61C2×D411yescharacteristic
209C22×Dic61C2×D411yescharacteristic
210C2×D244—22no—
211C2×D244—22no—
212C2×D244—21no—
213C2×D244—24no—
214C2×D244—82no—
215C2×D244C2412yes—
216C2×C4×D61—22no—
217C2×C4×D61—22no—
218C2×C4×D61—24no—
219C2×C4×D61—82no—
220C2×C4×D61C2×D412yes—
221C2×C4×D61C2412yes—
222C2×C8×C61—22no—
223C2×C8×C61—22no—
224C2×C8×C61C2412yes—
225C2×C8×C61C2412yes—
226C4⋊C4×C61—21no—
227C4⋊C4×C61—21no—
228C4⋊C4×C61—24no—
229C4⋊C4×C61—24no—
230C4⋊C4×C61—21no—
231C4⋊C4×C61C2412yes—
232C4⋊C4×C61C2412yes—
233C4⋊C4×C61C2412yes—
234C22⋊C4×C61—24no—
235C22⋊Dic61C2×D414yes—
236#11758201—28no—
237#11758198—24no—
238#11758198—24no—
239#11758198—24no—
240#11758198—24no—
241#11758198—24no—
242#11758198—24no—
243#11758198C2×D414yes—
244C4⋊Dic61—21no—
245C4⋊Dic61—21no—
246C4⋊Dic61—24no—
247C4⋊Dic61—21no—
248C4⋊Dic61—24no—
249C4⋊Dic61—24no—
250C4⋊Dic61—24no—
251C4⋊Dic61C2412yes—
252C4⋊Dic61C2412yes—
253C4⋊Dic61C2412yes—
254#11758196—24no—
255#11758196—24no—
256#11758196—24no—
257#11758196C2×D414yes—
258C4×Dic61—24no—
259C4×Dic61—24no—
260C4×Dic61—24no—
261C4×Dic61C2×D412yes—
262C4×Dic61C2412yes—
263C2×#92418—22no—
264C2×#92418—28no—
265C2×#92418#4114yes—
266C2×#92418C2412yes—
267C2×#92418C2412yes—
268C8×D61—28no—
269C23×C61—22no—
270C23×C61—22no—
271C23×C61#13514yes—
272C23×C61C22×D412yes—
273C23×C61C22×D411yescharacteristic
274C22×D61—22no—
275C22×D61—22no—
276C22×D61—22no—
277C22×D61—22no—
278C22×D61—42no—
279C22×D61—42no—
280C22×D61—42no—
281C22×D61C22×D412yes—
282Q8×C61—22no—
283Q8×C61—22no—
284Q8×C61—42no—
285C2×C4×C61—22no—
286C2×C4×C61—24no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—22no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—42no—
294C2×C4×C61—42no—
295C2×C4×C61—42no—
296C2×C4×C61—42no—
297C2×C4×C61—84no—
298C2×C4×C61C22×D412yes—
299C2×C4×C61C22×D411yescharacteristic
300C2×C4×C61C2×#4112yes—
301C2×C4×C612−1+412yes—
302C2×C4×C61C2511yescharacteristic
303C22⋊D61—28no—
304C22⋊D61—48no—
305C2×Dic61—22no—
306C2×Dic61—22no—
307C2×Dic61—22no—
308C2×Dic61—22no—
309C2×Dic61—22no—
310C2×Dic61—22no—
311C2×Dic61—48no—
312C2×Dic61—42no—
313C2×Dic61—42no—
314C2×Dic61—42no—
315C2×Dic61C22×D412yes—
316C2×Dic61C22×D412yes—
317C2×Dic61C22×D412yes—
318D244—22no—
319D244—22no—
320D244—42no—
321D244—84no—
322C4×D61—24no—
323C4×D61—22no—
324C4×D61—22no—
325C4×D61—84no—
326C8×C61—22no—
327C8×C61—22no—
328#92418—22no—
329#92418C2×#4114yes—
330C2×#3337—611nomaximal, Sylow
331C22×C61—28no—
332C22×C61—22no—
333C22×C61—22no—
334C22×C61#54712yes—
335C22×C61C2×#13514yes—
336C22×C61C2×#13512yes—
337C22×C61#57712yes—
338C22×C61C23×D411yescharacteristic
339C2×D61—22no—
340C2×D61—22no—
341C2×D61—22no—
342C2×D61—44no—
343C2×D61—42no—
344C2×D61—42no—
345C2×D61—42no—
346C2×D61—84no—
347C4×C61—22no—
348C4×C61—42no—
349C4×C61—42no—
350C4×C61—42no—
351C4×C61—42no—
352C4×C61#54712yes—
353C4×C61C22×#4111yescharacteristic
354C4×C61C2×2−1+411yescharacteristic
355Dic61—22no—
356Dic61—22no—
357Dic61—22no—
358Dic61—42no—
359Dic61—42no—
360Dic61—42no—
361C2×#553—611no—
362C2×#552—611no—
363#3337—6116no—
364C2×#499—611no—
365C2×#484D6111yescharacteristic, complemented
366C2×#485—611no—
367C2×#482—611no—
368C2×#480—611no—
369C2×#479—611no—
370C2×#478—611no—
371C2×#465—611no—
372C2×#465—611no—
373C2×C4×SD16—611no—
374C2×C8×D4—611no—
375C2×#427—611no—
376C22×#106—611no—
377C2×C61—24no—
378C2×C61#333714yescomplemented
379C2×C61C2×#54711yescharacteristic
380C2×C61C22×#13511yescharacteristic
381C2×C61C2×#57711yescharacteristic
382D61—42no—
383D61—82no—
384C22×SD16—611no—
385C23×C8—611no—
386C23×C8—611no—
387#553—618no—
388#553—1224no—
389#552—618no—
390#552—1224no—
391C2×#126—1221no—
392C2×#126—1221no—
393C2×#125—611no—
394C2×#125—611no—
395C2×#125—1221no—
396C2×#123—1221no—
397C2×#123—1221no—
398C2×C22⋊Q8—611no—
399C2×C22⋊Q8C2×D6111yescharacteristic
400C2×#121—611no—
401C2×#121—611no—
402C2×#121—1221no—
403C2×C4×Q8—611no—
404C2×C4×D4—611no—
405C2×C4×D4—611no—
406C2×C4×D4—1221no—
407C2×#117—611no—
408C2×#117—611no—
409C2×#117—1221no—
410C22×C4⋊C4—611no—
411C22×C4⋊C4C2×D6111yescharacteristic
412#499—618no—
413#485—618no—
414#484C2×D6118yescomplemented
415#482—618no—
416#480—618no—
417#479—618no—
418#478—618no—
419#465—618no—
420#465—618no—
421C4×SD16—618no—
422C8×D4—618no—
423#427—618no—
424C2×#107—611no—
425C2×#107—611no—
426C2×#107C2×D6111yescharacteristic
427C2×#107C2×D6111yescharacteristic
428C2×#106—611no—
429C2×#106—611no—
430C2×#106—618no—
431C2×#106—611no—
432C2×#106—611no—
433C2×#106—611no—
434C2×C4⋊C8—611no—
435C2×#103—611no—
436C2×#103C2×D6111yescharacteristic
437C2×#103C2×D6111yescharacteristic
438C2×#102—611no—
439C2×#102—611no—
440C2×#102—611no—
441C2×C22⋊C8—611no—
442C2×C22⋊C8C2×D6111yescharacteristic
443C2×C4×C8—611no—
444C61C2×#333711yescharacteristic, complemented, Sylow
445C22×Q8C22×D6111yescharacteristic
446C22×D4—611no—
447C22×D4—611no—
448C22×D4—1221no—
449C22×D4—1221no—
450C23×C4—21no—
451C23×C4—611no—
452C23×C4—1221no—
453C23×C4—1221no—
454C23×C4C22×D6111yescharacteristic
455C2×SD16—614no—
456C2×SD16—1224no—
457C22×C8—611no—
458C22×C8—611no—
459C22×C8—614no—
460C22×C8—614no—
461C22×C8—1224no—
462C22×C8—1224no—
463C22×C8C22×D6111yescharacteristic
464C22×C8C22×D6111yescharacteristic
465#126—1228no—
466#126—1228no—
467#125—614no—
468#125—614no—
469#125—1222no—
470#125—1222no—
471#125—1228no—
472#123—1228no—
473#123—1228no—
474C22⋊Q8—22no—
475C22⋊Q8—614no—
476C22⋊Q8—1222no—
477C22⋊Q8C22×D6114yes—
478#121—614no—
479#121—614no—
480#121—1222no—
481#121—1228no—
482#121—1222no—
483C4×Q8—614no—
484C4×Q8—1222no—
485C4×D4—614no—
486C4×D4—614no—
487C4×D4—614no—
488C4×D4—1222no—
489C4×D4—1228no—
490#117—614no—
491#117—614no—
492#117—1228no—
493#117—1222no—
494#117—1222no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—611no—
499C2×C4⋊C4—611no—
500C2×C4⋊C4—611no—
501C2×C4⋊C4—614no—
502C2×C4⋊C4—611no—
503C2×C4⋊C4—1221no—
504C2×C4⋊C4—1221no—
505C2×C4⋊C4—1221no—
506C2×C4⋊C4—1221no—
507C2×C4⋊C4—1221no—
508C2×C4⋊C4—1221no—
509C2×C4⋊C4—1221no—
510C2×C4⋊C4—1222no—
511C2×C4⋊C4C22×D6111yescharacteristic
512C2×C4⋊C4C22×D6111yescharacteristic
513C2×C4⋊C4C22×D6114yes—
514C2×C4⋊C4C22×D6111yescharacteristic
515C2×C22⋊C4—21no—
516C2×C22⋊C4—611no—
517C2×C22⋊C4—611no—
518C2×C22⋊C4—1221no—
519C2×C22⋊C4—1221no—
520C2×C22⋊C4—1221no—
521C2×C22⋊C4—1221no—
522C2×C22⋊C4—1221no—
523C2×C22⋊C4—1221no—
524C2×C42—611no—
525C2×C42—1221no—
526C2×C42—1221no—
527C2×C42—1221no—
528#107—614no—
529#107—614no—
530#107C22×D6114yes—
531#107C22×D6114yes—
532#106—614no—
533#106—614no—
534#106—614no—
535#106—614no—
536#106—614no—
537C4⋊C8—614no—
538#103—614no—
539#103C22×D6114yes—
540#103C22×D6114yes—
541#102—614no—
542#102—614no—
543#102—614no—
544C22⋊C8—614no—
545C22⋊C8C22×D6114yes—
546C4×C8—614no—
547C24—611no—
548C24—1221no—
549C24D4×D6111yescharacteristic
550C2×Q8—21no—
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8C23×D6112yes—
554C2×D4—614no—
555C2×D4—612no—
556C2×D4—1224no—
557C2×D4—1224no—
558C2×D4—1224no—
559C2×D4—1221no—
560C2×D4—1222no—
561C2×D4—1222no—
562C2×D4—4882no—
563C2×D4—2444no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—24no—
571C22×C4—82no—
572C22×C4—611no—
573C22×C4—611no—
574C22×C4—611no—
575C22×C4—612no—
576C22×C4—612no—
577C22×C4—1224no—
578C22×C4—1222no—
579C22×C4—1222no—
580C22×C4—1224no—
581C22×C4—1221no—
582C22×C4—1221no—
583C22×C4—1221no—
584C22×C4—4882no—
585C22×C4—2444no—
586C22×C4D4×D6112yes—
587C22×C4D4×D6111yescharacteristic
588C22×C4C23×D6112yes—
589C22×C4C23×D6111yescharacteristic
590SD16—1228no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—614no—
594C2×C8—612no—
595C2×C8—612no—
596C2×C8—1228no—
597C2×C8—1228no—
598C2×C8—1222no—
599C2×C8C23×D6112yes—
600C2×C8C23×D6112yes—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—21no—
606C4⋊C4—614no—
607C4⋊C4—612no—
608C4⋊C4—612no—
609C4⋊C4—612no—
610C4⋊C4—1224no—
611C4⋊C4—1224no—
612C4⋊C4—1224no—
613C4⋊C4—1224no—
614C4⋊C4—1224no—
615C4⋊C4—1224no—
616C4⋊C4—1221no—
617C4⋊C4—1221no—
618C4⋊C4—1224no—
619C4⋊C4—1221no—
620C4⋊C4C23×D6112yes—
621C4⋊C4C23×D6112yes—
622C4⋊C4C23×D6112yes—
623C22⋊C4—24no—
624C22⋊C4—614no—
625C22⋊C4—614no—
626C22⋊C4—1224no—
627C22⋊C4—1224no—
628C22⋊C4—1224no—
629C22⋊C4—1224no—
630C22⋊C4—1224no—
631C22⋊C4—1224no—
632C42—612no—
633C42—612no—
634C42—1224no—
635C42—1224no—
636C42—1224no—
637C23—22no—
638C23—22no—
639C23—612no—
640C23—1222no—
641C23—1222no—
642C23—1222no—
643C23—1222no—
644C23—2442no—
645C23—2442no—
646C23—2442no—
647C23#1451980014yes—
648C23C2×D4×D6112yes—
649C23C2×D4×D6111yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—42no—
653D4—1228no—
654D4—1222no—
655D4—1222no—
656D4—4884no—
657D4—2448no—
658D4—2442no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—24no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—84no—
672C2×C4—612no—
673C2×C4—612no—
674C2×C4—612no—
675C2×C4—1222no—
676C2×C4—1222no—
677C2×C4—1222no—
678C2×C4—1222no—
679C2×C4—1222no—
680C2×C4—1224no—
681C2×C4—1222no—
682C2×C4—1222no—
683C2×C4—1222no—
684C2×C4—4884no—
685C2×C4—2448no—
686C2×C4—2442no—
687C2×C4—2442no—
688C2×C4—2442no—
689C2×C4C2×D4×D6112yes—
690C2×C4C2×D4×D6111yescharacteristic
691C2×C4#41×D6112yes—
692C2×C4#1451982412yes—
693C2×C4C24×D6111yescharacteristic
694C8—22no—
695C8—22no—
696C8—614no—
697C8—1222no—
698C22—28no—
699C22—22no—
700C22—22no—
701C22—1222no—
702C22—1222no—
703C22—1222no—
704C22—4884no—
705C22—2442no—
706C22—2442no—
707C22—2442no—
708C22—2444no—
709C22#1684041012yes—
710C22C2×#1451980014yes—
711C22C2×#1451980012yes—
712C22#1684057212yes—
713C22C22×D4×D6111yescharacteristic
714C4—22no—
715C4—42no—
716C4—42no—
717C4—42no—
718C4—42no—
719C4—1222no—
720C4—1222no—
721C4—1222no—
722C4—2442no—
723C4—2442no—
724C4—2442no—
725C4#1684041012yes—
726C4C2×#41×D6111yescharacteristic
727C4C2×#1451982411yescharacteristic
728C2—24no—
729C2—4882no—
730C2—2442no—
731C2#2145819614yesdirect product factor
732C2C2×#1684041011yescharacteristic
733C2C22×#1451980011yescharacteristic
734C2C2×#1684057211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#484C2
socleC23×C61C22×D4
prime radicalC2×#16840460C2
hypercenterC2×#484D61
hypocenterC61C2×#3337
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#484

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#16840454C2semidirect
3. #21458196C2direct (N × H)
4. C2×#16840163C2semidirect
5. C2×#16840102C2semidirect
6. C2×#16840089C2semidirect
7. C2×#16840076C2semidirect
8. C2×#16840071C2semidirect
9. C2×#16840065C2semidirect
10. C2×#16839994C2semidirect
11. C2×#16839993C2semidirect
12. C2×#16839847C2semidirect
13. C2×#16839825C2semidirect
14. C2×#16839799C2semidirect
15. C22×#14519708C2semidirect
16. C2×C61×#484C2semidirect
23. #16840454C22semidirect
43. #16840163C22semidirect
44. #16840102C22semidirect
45. #16840089C22semidirect
46. #16840076C22semidirect
47. #16840071C22semidirect
48. #16840065C22semidirect
49. #16839994C22semidirect
50. #16839993C22semidirect
51. #16839847C22semidirect
52. #16839825C22semidirect
53. #16839799C22semidirect
61. C2×#14519708C22semidirect
71. C61×#484C22semidirect
365. C2×#484D61semidirect
378. C2×C61#3337semidirect
414. #484C2×D61semidirect
444. C61C2×#3337semidirect
731. C2#21458196direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#168404602
C2×#168404542
#214581962
C2×#168401632
C2×#168401022
C2×#168400892
C2×#168400762
C2×#168400712
C2×#168400652
C2×#168399942
C2×#168399932
C2×#168398472
C2×#168398252
C2×#168397992
C22×#145197082
C2×C61×#4842
C2×#333761